Possible Duplicate:
examples of measurable functions on $\mathbb{R}$
Is there a measurable function $g:\mathbb{R} \to \mathbb{R} ^{+}$ such that $\int_{[a,b]}g dx=\infty$ $\forall a\neq b \in\mathbb{R}$ .
Asked
Active
Viewed 151 times
4
-
Are we assuming Lebesgue measure? – Gautam Shenoy Nov 22 '12 at 15:34
-
yes I will edit it – omar Nov 22 '12 at 15:38
-
Clearly g cannot be continuous... – Gautam Shenoy Nov 22 '12 at 15:40
-
Yes otherwise it will have a maximum by the extreme value theorem – Amr Nov 22 '12 at 15:42
-
4See: http://math.stackexchange.com/q/24413 – Nov 22 '12 at 15:43